Getting your Trinity Audio player ready...

Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

Waves - Case Studies - help10

The speed of a wave in a rope is affected by the properties of the rope - mainly, how tight it is pulled (tension) and its mass per length (linear density). Changes in either of these properties changes the wave speed. For a fixed frequency, a change in the wave speed will also change the wavelength of the wave.

There are three similar versions of this question. Here is one of the versions:

Version 1:

The diagram at the right is a snapshot in time of a wave moving along a rope. Which diagram below represents a wave with the same frequency and moving through the same rope that is pulled to one-fourth the tension? Tap on an image to select or deselect it.

You have to make some decisions to be successful with this question. First you have to decide on how one-fourth the tension affects the speed. Then you have to decide the affect of this speed change on wavelength. And finally, you have to decide which diagram displays such a wavelength.

How Does Tension Affect Speed?
In this question, the tension with which the ropes held is quartered (one-fourth as large). The speed of a wave in a rope depends upon the tension at which the rope is held. The relatonship is that speed is proportional to the square root of tension. So a quartering of the tension causes the speed to halve or be one-half as fast.

The Effect of Speed on Wavelength
In this question, the frequency at which the rope vibrates is not changed. For a constant frequency, a change in speed will affect the wavelength. Speed and wavelength are directly proportional to each other. So a halving of speed causes a halving of wavelength. You need to select the wave pattern that shows one-half the wavelength.

Deciding on a Diagram
You can use the background grid to determine the wavelength of the wave. You can count the squares. It can be thought of as the distance between one crest and the next adjacent crest. Once you determine the wavelength in the given diagram, it's time to select the answer. The previous section on this Help page describe what type of wavelength you are looking for. You can do the square counting again to determine which pattern displays such a wavelength.

Try these links to The Physics Classroom Tutorial for more help with understanding wave properties:

The Anatomy of a Wave (wavelength and amplitude)

The Speed of a Wave

The Wave Equation